You want your portfolio beta to be $1\mathrm{.}08.$ Currently, your portfolio

consists of $$3,000$ invested in stock A with a beta of $1\mathrm{.}60$ and

$$2,000$ in stock $B$ with a beta of $0\mathrm{.}70.$ You have another $$5,000$ to

invest and want to divide it between an asset with a beta of

$1\mathrm{.}42$ and a risk$-$free asset. How much should you invest in the risk$-$

free asset?